Of interest in this connection would be to see whether the LQG analogue of Minkowski spacetime breaks or preserves global Lorentz invariance, and Carlo Rovelli and coworkers have recently been investigating the Minkowski state of LQG using spin-foam techniques.
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Giovanni Amelino-Camelia then proposed that the mystery of ultra-high-energy cosmic rays might be solved by assuming such violations of the special-relativity dispersion relation for photons.
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